Recall that the exponentially weighted averaging forecaster (EWAF) is equivalent to the Follow The Regularized Leader (FTRL) algorithm with entropic regularization [1]}, [2]}.
More generally, per Lemma REF , it is easy to show that the exponentially weighted averaging forecaster (EWAF) for \(d\)  experts with initial weights \(w_{0,1}, ... w_{0,d}\) , corresponds to Follow The Regularized Leader (FTRL) algorithm with the generalized entropic regularization term
\(\mathcal {R}(p) = \sum _{j=1}^d p_j \ln p_j - p_j \ln w_{0,j}.\) 
